MAYBE
Time: 0.113883
TRS:
 {app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
          app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
          app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
                  app(app(app(app(f(), 0()), y), 0()), u) -> true(),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
        app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                             app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                                     app(perfectp(), 0()) -> false()}
 DP:
  DP:
   {app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z),
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(app(f(), x), app(s(), 0())), app(s(), x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(f(), x), app(s(), 0())),
                               app#(perfectp(), app(s(), x)) -> app#(f(), x),
                               app#(perfectp(), app(s(), x)) -> app#(s(), 0())}
  TRS:
  {app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
           app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
           app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
                   app(app(app(app(f(), 0()), y), 0()), u) -> true(),
        app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
         app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
             app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                               app(app(map(), fun), nil()) -> nil(),
          app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                            app(app(filter(), fun), nil()) -> nil(),
                              app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                                      app(perfectp(), 0()) -> false()}
  UR:
   {app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
            app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
            app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
                    app(app(app(app(f(), 0()), y), 0()), u) -> true(),
         app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
          app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
              app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                app(app(map(), fun), nil()) -> nil(),
           app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                             app(app(filter(), fun), nil()) -> nil(),
                               app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                                       app(perfectp(), 0()) -> false(),
                                                    a(w, v) -> w,
                                                    a(w, v) -> v}
   EDG:
    {
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
     (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(s(), 0()))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(f(), x), app(s(), 0())))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(f(), x), app(s(), 0())), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(f(), x), app(s(), 0())), app(s(), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(f(), x), app(s(), 0())))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(f(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(s(), 0()))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
     (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
     (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
    }
    STATUS:
     arrows: 0.903750
     SCCS (2):
      Scc:
       {app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
         app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
      Scc:
       {app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
                app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u)}
      
      SCC (6):
       Strict:
        {app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
       Weak:
       {app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
                app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
                app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
                        app(app(app(app(f(), 0()), y), 0()), u) -> true(),
             app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
              app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
                  app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                    app(app(map(), fun), nil()) -> nil(),
               app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                 app(app(filter(), fun), nil()) -> nil(),
                                   app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                                           app(perfectp(), 0()) -> false()}
       Open
      
      
      
      
      
      
      
      
      
      
      
      SCC (2):
       Strict:
        {app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
                 app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u)}
       Weak:
       {app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
                app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
                app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
                        app(app(app(app(f(), 0()), y), 0()), u) -> true(),
             app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
              app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
                  app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                    app(app(map(), fun), nil()) -> nil(),
               app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                 app(app(filter(), fun), nil()) -> nil(),
                                   app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                                           app(perfectp(), 0()) -> false()}
       Open